Distributed Model Predictive Control for Plant-Wide Systems
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SHAOYUAN LI Shanghai Jiao Tong University, China
YI ZHENG Shanghai Jiao Tong University, China
Content
About the Authors xv
Acknowledgement xvii
List of Figures xix
List of Tables xxiii
1 Introduction 1
1.1 Plant-Wide System 1
1.2 Control System Structure of the Plant-Wide System 3
1.2.1 Centralized Control 4
1.2.2 Decentralized Control and Hierarchical Coordinated Decentralized Control 5
1.2.3 Distributed Control 6
1.3 Predictive Control 8
1.3.1 What is Predictive Control 8
1.3.2 Advantage of Predictive Control 9
1.4 Distributed Predictive Control 9
1.4.1 Why Distributed Predictive Control 9
1.4.2 What is Distributed Predictive Control 10
1.4.3 Advantage of Distributed Predictive Control 10
1.4.4 Classification of DMPC 11
1.5 About this Book 13
Part I FOUNDATION
2 Model Predictive Control 19
2.1 Introduction 19
2.2 Dynamic Matrix Control 20
2.2.1 Step Response Model 20
2.2.2 Prediction 21
2.2.3 Optimization 22
2.2.4 Feedback Correction 23
2.2.5 DMC with Constraint 24
2.3 Predictive Control with the State Space Model 26
2.3.1 System Model 27
2.3.2 Performance Index 28
2.3.3 Prediction 28
2.3.4 Closed-Loop Solution 30
2.3.5 State Space MPC with Constraint 31
2.4 Dual Mode Predictive Control 33
2.4.1 Invariant Region 33
2.4.2 MPC Formulation 34
2.4.3 Algorithms 35
2.4.4 Feasibility and Stability 36
2.5 Conclusion 37
3 Control Structure of Distributed MPC 39
3.1 Introduction 39
3.2 Centralized MPC 40
3.3 Single-Layer Distributed MPC 41
3.4 Hierarchical Distributed MPC 42
3.5 Example of the Hierarchical DMPC Structure 43
3.6 Conclusion 45
4 Structure Model and System Decomposition 47
4.1 Introduction 47
4.2 System Mathematic Model 48
4.3 Structure Model and Structure Controllability 50
4.3.1 Structure Model 50
4.3.2 Function of the Structure Model in System Decomposition 51
4.3.3 Input-Output Accessibility 53
4.3.4 General Rank of the Structure Matrix 56
4.3.5 Structure Controllability 56
4.4 Related Gain Array Decomposition 58
4.4.1 RGA Definition 59
4.4.2 RGA Interpretation 60
4.4.3 Pairing Rules 61
4.5 Conclusion 63
Part II UNCONSTRAINED DISTRIBUTED PREDICTIVE CONTROL
5 Local Cost Optimization-based Distributed Model Predictive Control 67
5.1 Introduction 67
5.2 Local Cost Optimization-based Distributed Predictive Control 68
5.2.1 Problem Description 68
5.2.2 DMPC Formulation 69
5.2.3 Closed-loop Solution 72
5.2.4 Stability Analysis 79
5.2.5 Simulation Results 79
5.3 Distributed MPC Strategy Based on Nash Optimality 82
5.3.1 Formulation 83
5.3.2 Algorithm 86
5.3.3 Computational Convergence for Linear Systems 86
5.3.4 Nominal Stability of Distributed Model Predictive Control System 88
5.3.5 Performance Analysis with Single-step Horizon Control Under Communication Failure 89
5.3.6 Simulation Results 94
5.4 Conclusion 99
Appendix 99
Appendix A. QP problem transformation 99
Appendix B. Proof of Theorem 5.1 100
6 Cooperative Distributed Predictive Control 103
6.1 Introduction 103
6.2 Noniterative Cooperative DMPC 104
6.2.1 System Description 104
6.2.2 Formulation 104
6.2.3 Closed-Form Solution 107
6.2.4 Stability and Performance Analysis 109
6.2.5 Example 113
6.3 Distributed Predictive Control based on Pareto Optimality 114
6.3.1 Formulation 118
6.3.2 Algorithm 119
6.3.3 The DMPC Algorithm Based on Plant-Wide Optimality 119
6.3.4 The Convergence Analysis of the Algorithm 121
6.4 Simulation 121
6.5 Conclusions 123
7 Networked Distributed Predictive Control with Information Structure Constraints 125
7.1 Introduction 125
7.2 Noniterative Networked DMPC 126
7.2.1 Problem Description 126
7.2.2 DMPC Formulation 127
7.2.3 Closed-Form Solution 132
7.2.4 Stability Analysis 135
7.2.5 Analysis of Performance 135
7.2.6 Numerical Validation 137
7.3 Networked DMPC with Iterative Algorithm 144
7.3.1 Problem Description 144
7.3.2 DMPC Formulation 145
7.3.3 Networked MPC Algorithm 147
7.3.4 Convergence and Optimality Analysis for Networked 150
7.3.5 Nominal Stability Analysis for Distributed Control Systems 152
7.3.6 Simulation Study 153
7.4 Conclusion 159
Appendix 159
Appendix A. Proof of Lemma 7.1 159
Appendix B. Proof of Lemma 7.2 160
Appendix C. Proof of Lemma 7.3 160
Appendix D. Proof of Theorem 7.1 161
Appendix E. Proof of Theorem 7.2 161
Appendix F. Derivation of the QP problem (7.52) 164
Part III CONSTRAINT DISTRIBUTED PREDICTIVE CONTROL
8 Local Cost Optimization Based Distributed Predictive Control with Constraints 169
8.1 Introduction 169
8.2 Problem Description 170
8.3 Stabilizing Dual Mode Noncooperative DMPC with Input Constraints 171
8.3.1 Formulation 171
8.3.2 Algorithm Design for Resolving Each Subsystem-based Predictive Control 176
8.4 Analysis 177
8.4.1 Recursive Feasibility of Each Subsystem-based Predictive Control 177
8.4.2 Stability Analysis of Entire Closed-loop System 183
8.5 Example 184
8.5.1 The System 184
8.5.2 Performance Comparison with the Centralized MPC 185
8.6 Conclusion 187
9 Cooperative Distributed Predictive Control with Constraints 189
9.1 Introduction 189
9.2 System Description 190
9.3 Stabilizing Cooperative DMPC with Input Constraints 191
9.3.1 Formulation 191
9.3.2 Constraint C-DMPC Algorithm 193
9.4 Analysis 194
9.4.1 Feasibility 194
9.4.2 Stability 199
9.5 Simulation 201
9.6 Conclusion 208
10 Networked Distributed Predictive Control with Inputs and Information Structure Constraints 209
10.1 Introduction 209
10.2 Problem Description 210
10.3 Constrained N-DMPC 212
10.3.1 Formulation 212
10.3.2 Algorithm Design for Resolving Each Subsystem-based Predictive Control 218
10.4 Analysis 219
10.4.1 Feasibility 219
10.4.2 Stability 225
10.5 Formulations Under Other Coordination Strategies 227
10.5.1 Local Cost Optimization Based DMPC 227
10.5.2 Cooperative DMPC 228
10.6 Simulation Results 229
10.6.1 The System 229
10.6.2 Performance of Closed-loop System under the N-DMPC 230
10.6.3 Performance Comparison with the Centralized MPC and the Local Cost Optimization based MPC 231
10.7 Conclusions 236
Part IV APPLICATION
11 Hot-Rolled Strip Laminar Cooling Process with Distributed Predictive Control 239
11.1 Introduction 239
11.2 Laminar Cooling of Hot-rolled Strip 240
11.2.1 Description 240
11.2.2 Thermodynamic Model 241
11.2.3 Problem Statement 242
11.3 Control Strategy of HSLC 244
11.3.1 State Space Model of Subsystems 244
11.3.2 Design of Extended Kalman Filter 247
11.3.3 Predictor 247
11.3.4 Local MPC Formulation 248
11.3.5 Iterative Algorithm 249
11.4 Numerical Experiment 251
11.4.1 Validation of Designed Model 251
11.4.2 Convergence of EKF 252
11.4.3 Performance of DMPC Comparing with Centralized MPC 252
11.4.4 Advantages of the Proposed DMPC Framework Comparing with the Existing Method 253
11.5 Experimental Results 256
11.6 Conclusion 258
12 High-Speed Train Control with Distributed Predictive Control 263
12.1 Introduction 263
12.2 System Description 264
12.3 N-DMPC for High-Speed Trains 264
12.3.1 Three Types of Force 264
12.3.2 The Force Analysis of EMUs 266
12.3.3 Model of CRH2 267
12.3.4 Performance Index 271
12.3.5 Optimization Problem 272
12.4 Simulation Results 272
12.4.1 Parameters of CRH2 273
12.4.2 Simulation Matrix 273
12.4.3 Results and Some Comments 274
12.5 Conclusion 278
13 Operation Optimization of Multitype Cooling Source System Based on DMPC 279
13.1 Introduction 279
13.2 Structure of Joint Cooling System 279
13.3 Control Strategy of Joint Cooling System 280
13.3.1 Economic Optimization Strategy 281
13.3.2 Design of Distributed Model Predictive Control in Multitype Cold Source System 283
13.4 Results and Analysis of Simulation 286
13.5 Conclusion 292
References 293
Index 299
List of Figures
- Figure 1 The schematic of distributed model predictive control
- Figure 1.1 The wind farm
- Figure 1.2 The multizone building temperature regulation system
- Figure 1.3 Distributed power generation power network
- Figure 1.4 Hierarchical control system for the plant-wide system
- Figure 1.5 Centralized control
- Figure 1.6 Decentralized control
- Figure 1.7 Hierarchical coordinated decentralized control
- Figure 1.8 Distributed control
- Figure 1.9 Distributed control in the hierarchical control system
- Figure 1.10 Distributed predictive control
- Figure 1.11 Content of this book
- Figure 2.1 A state observer with measurable disturbances
- Figure 3.1 The centralized MPC control structure
- Figure 3.2 The single-layer decentralized/distributed MPC control structure
- Figure 3.3 The hierarchical decentralized/distributed MPC control structure
- Figure 3.4 Simplified process flow diagram of a hydrocracking plant and its hierarchical distributed MPC control structure
- Figure 4.1 The schematic of the distributed system
- Figure 4.2 A multizone building temperature regulation system
- Figure 4.3 The two-input-two-output system (TITO)
- Figure 4.4 Distillation column controlled with the LV-configuration
- Figure 5.1 Maximum closed-loop eigenvalues with LCO-DMPC when a = 0.1
- Figure 5.3 Maximum closed-loop eigenvalues with LCO-DMPC when a = 1
- Figure 5.2 Performance with ? = 1 and P = 20 of a closed-loop system under the control of LCO-DMPC with a = 0.1
- Figure 5.4 Performance with ? = 1 and P = 20 of a closed-loop system under the control of LCO-DMPC with a = 1
- Figure 5.5 Shell heavy oil fractionator benchmark control problem
- Figure 5.6 Closed-loop system output responses and manipulated/control signals with no communication failure under the disturbance pattern d1 = [0.5 0.5]T
- Figure 5.7 Closed-loop system output responses and manipulated/control signals with no communication failure under the disturbance pattern d1 = [-0.5 -0.5]T
- Figure 5.8 Closed-loop system output responses and manipulated/control signals with mixed communication failure under the disturbance pattern d1 = [0.5 0.5]T
- Figure 5.9 Closed-loop system output responses and manipulated/control signals with mixed communication failure under the disturbance pattern d1 = [-0.5 -0.5]T
- Figure 6.1 Plant with a = 0.1: (a) maximum closed-loop eigenvalues with LCO-DMPC and C-DMPC; (b) control performance with ? = 1 for LCO-DMPC (blue line, MSE = 0.2568) and C-DMPC (red line, MSE = 0.2086).
- Figure 6.2 Plant with a = 1: (a) maximum closed-loop eigenvalues with LCO-DMPC and C-DMPC; (b) control performance with ? = 1 for LCO-DMPC (blue line, MSE = 0.2277) and C-DMPC (red line, MSE = 0.2034).
- Figure 6.3 Plant with a = 10: (a) maximum closed-loop eigenvalues with LCO-DMPC and C-DMPC; (b) control performance with ? = 1 for LCO-DMPC (blue line, unstable) and C-DMPC (red line, MSE = 0. 1544).
- Figure 6.4 The outputs and inputs of each subprocess
- Figure 6.5 The outputs and inputs of the second subprocess
- Figure 7.1 ACC process for middle and heavy plates
- Figure 7.2 Flux of each header unit using centralized MPC, N-DMPC, and LCO-MPC
- Figure 7.3 Control strategy of ACC
- Figure 7.4 Equilibriums of states of entire system
- Figure 7.5 Performance of close-loop subsystems using centralized MPC, N-DMPC, and the LCO-MPC
- Figure 7.6 Diagram of a serially connected process
- Figure 7.7 Diagram of the MPC unit for each subsystem
- Figure 7.8 Diagram of networked MPC algorithm
- Figure 7.9 Outputs and control signals under the N-DMPC iterative algorithm
- Figure 7.10 Outputs and control signals under the decentralized MPC
- Figure 7.11 Outputs and control signals under the LCO-DMPC with Nash optimization
- Figure 7.12 Performance index comparisons for three schemes
- Figure 7.13 Structure of a walking beam reheating furnace
- Figure 7.14 Furnace temperature and fuel feed flow for each zone
- Figure 8.1 The interaction relationship among subsystems
- Figure 8.2 The evolution of the states under the LCO-DMPC
- Figure 8.3 The evolution of the control inputs under the LCO-DMPC
- Figure 8.4 The evolution of the states under the centralized MPC
- Figure 8.5 The evolution of the control inputs under the centralized MPC
- Figure 9.1 Schematic of the discrepancy among feasible state sequence and presumed state sequence
- Figure 9.2 The multizone building temperature regulation system
- Figure 9.3 The evolution of the states under the centralized MPC, LCO-DMPC, and C-DMPC
- Figure 9.4 The evolution of the inputs under the centralized MPC, LCO-DMPC, and C-DMPC
- Figure 9.5 Differences of the absolute value of the state and inputs of each subsystem between under the control of LCO-DMPC and under the control of centralized MPC, and between under the control of C-DMPC and under the control centralized DMPC
- Figure 9.6 The difference between the input of each subsystem produced by the LCO-DMPC and the input of each subsystem calculated by the centralized MPC, and between the input of each subsystem produced by the C-DMPC and the input of each subsystem calculated by the centralized MPC
- Figure 10.1 The interaction relationship among subsystems
- Figure 10.2 The evolution of the states under the N-DMPC
- Figure 10.3 The evolution of the control inputs under the N-DMPC
- Figure 10.4 The evolution of the states under the centralized MPC
- Figure 10.5 The evolution of the control inputs under the centralized MPC
- Figure 10.6 The evolution of the states under the LCO-DMPC
- Figure 10.7 The evolution of the control inputs under the LCO-DMPC
- Figure 10.8 The errors between the absolute value of the state of each subsystem under the centralized MPC and the absolute value of the state of each subsystem under the N-DMPC
- Figure 10.9 The difference between the input of each subsystem produced by the centralized MPC and the input of each subsystem calculated by the N-DMPC
- Figure 10.10 The errors between the absolute value of the state of each subsystem under the local cost optimization based DMPC and the absolute value of the state of each subsystem under the N-DMPC
- Figure 10.11 The difference between the input of each subsystem produced by the LCO-DMPC and the input of each subsystem calculated by the N-DMPC
- Figure 11.1 Hot-rolled strip laminar cooling process
- Figure 11.2 Desired temperature profile
- Figure 11.3 The structure of DMPC framework for HSLC
- Figure 11.4 The division of each subsystem
- Figure 11.5 Comparison between the predictive CT and the measurement of CT
- Figure 11.6 Initial states of process model and observer
- Figure 11.7 Comparison of temperatures estimated by process model and observer
- Figure 11.8 Performance comparison of different control strategies (centralized MPC and DMPC framework proposed)
- Figure 11.9 Flux of each header group with centralized MPC and DMPC framework proposed
- Figure 11.10 The cooling curve of each strip-point with existing method
- Figure 11.11 The cooling curve of each strip-point with the proposed DMPC framework
- Figure 11.12 The structure of experimental system
- Figure 11.13 Runout table pilot apparatus
- Figure 11.14 Finishing rolling temperature of strip
- Figure 11.16 Flux of each header group with DMPC framework
- Figure 12.1 Traction characteristics of the CRH2 10
- Figure 12.2 Groups of CRH2 ("M" means motor coach and "T" means trailer coach)
- Figure 12.3 Analysis of the force of the CRH2
- Figure 12.4 Spring-mass model
- Figure 12.5 The structure diagram of the distributed model predictive control
- Figure 12.6 Half of the CRH2 EMUs schematic diagram
- Figure 12.7 Velocity track
- Figure 12.8 Driving force optimal scheduling
- Figure 12.9 The relative displacement of the coaches
- Figure 12.10 Velocity track of the first coach
- Figure 12.13 Driving force optimal scheduling of the third coach
- Figure 12.12 Driving force optimal scheduling of the second coach
- Figure 12.11 Velocity track
- Figure 13.1 Structure of joint cooling system
- Figure 13.2 Control strategy of joint cooling...
